Electronvolt

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In physics, the electronvolt [1] [2] (symbol eV, also written electron-volt and electron volt) is a unit of energy equal to approximately 1.6×10−19 joules (symbol J) in SI units.

Physics is the natural science that studies matter and its motion and behavior through space and time and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

Because energy is defined via work, the SI unit for energy is the same as the unit of work – the joule (J), named in honor of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton metre and, in terms of SI base units

The joule is a derived unit of energy in the International System of Units. It is equal to the energy transferred to an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre. It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).

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Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences, because a particle with electric charge q has an energy E = qV after passing through the potential V; if q is quoted in integer units of the elementary charge and the potential in volts, one gets an energy in eV.

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges; positive and negative. Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.

Like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 J/C2h α / μ0 c0 . It is a common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics. It is commonly used with the metric prefixes milli-, kilo-, mega-, giga-, tera-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). In some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion (109) electronvolts; it is equivalent to the GeV.

The Planck constant is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299,792,458 metres per second. It is exact because by international agreement a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299792458 second. According to special relativity, c is the maximum speed at which all conventional matter and hence all known forms of information in the universe can travel. Though this speed is most commonly associated with light, it is in fact the speed at which all massless particles and changes of the associated fields travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. In the special and general theories of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.

Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors.

MeasurementUnitSI value of unit
EnergyeV1.6021766208(98)×10−19 J
MasseV/c21.782662×10−36 kg
MomentumeV/c5.344286×10−28 kg⋅m/s
TemperatureeV/kB1.1604505(20)×104 K
Timeħ/eV6.582119×10−16 s
Distanceħc/eV1.97327×10−7 m

Definition

An electronvolt is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. Hence, it has a value of one volt, 1 J/C, multiplied by the electron's elementary charge e, 1.6021766208(98)×10−19 C. [3] Therefore, one electronvolt is equal to 1.6021766208(98)×10−19 J. [4] The electronvolt, as opposed to volt, is not an SI unit. Its derivation is empirical, which means its value in SI units must be obtained by experiment and is therefore not known exactly, unlike the litre, the light-year and such other non-SI units. [5] Electonvolt (eV) is a unit of energy whereas volt (V) is the derived SI unit of electric potential. The SI unit for energy is joule (J). 1 eV is equal to 1.6021766208(98)×10−19 J

The electron is a subatomic particle, symbol
e
or
β
, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. As it is a fermion, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule per 1 coulomb. The official SI definition for volt uses power and current, where 1 volt = 1 watt per 1 ampere. This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

The elementary charge, usually denoted by e or sometimes qe, is the electric charge carried by a single proton, or equivalently, the magnitude of the electric charge carried by a single electron, which has charge e. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called the elementary positive charge. This charge has a measured value of approximately 1.6021766208(98)×10−19 C (coulombs). When the 2019 redefinition of SI base units takes effect on 20 May 2019, its value will be exactly1.602176634×10−19 C by definition of the coulomb. In the centimetre–gram–second system of units (CGS), it is 4.80320425(10)×10−10 statcoulombs.

Mass

By mass–energy equivalence, the electronvolt is also a unit of mass. It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c2, where c is the speed of light in vacuum (from E = mc2). It is common to simply express mass in terms of "eV" as a unit of mass, effectively using a system of natural units with c set to 1. [6] The mass equivalent of 1 eV/c2 is

In physics, mass–energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities directly relating to one another by Albert Einstein's famous formula:

Particle physics is a branch of physics that studies the nature of the particles that constitute matter and radiation. Although the word particle can refer to various types of very small objects, particle physics usually investigates the irreducibly smallest detectable particles and the fundamental interactions necessary to explain their behaviour. By our current understanding, these elementary particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model. Thus, modern particle physics generally investigates the Standard Model and its various possible extensions, e.g. to the newest "known" particle, the Higgs boson, or even to the oldest known force field, gravity.

In physics, natural units are physical units of measurement based only on universal physical constants. For example, the elementary charge e is a natural unit of electric charge, and the speed of light c is a natural unit of speed. A purely natural system of units has all of its units defined in this way, and usually such that the numerical values of the selected physical constants in terms of these units are exactly 1. These constants are then typically omitted from mathematical expressions of physical laws, and while this has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. It precludes the interpretation of an expression in terms of fundamental physical constants, such as e and c, unless it is known which units the expression is supposed to have. In this case, the reinsertion of the correct powers of e, c, etc., can be uniquely determined.

${\displaystyle 1\;{\text{eV}}/c^{2}={\frac {(1.60217646\times 10^{-19}\;{\text{C}})\cdot 1\;{\text{V}}}{(2.99792458\times 10^{8}\;{\text{m}}/{\text{s}})^{2}}}=1.783\times 10^{-36}\;{\text{kg}}.}$

For example, an electron and a positron, each with a mass of 0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy. The proton has a mass of 0.938 GeV/c2. In general, the masses of all hadrons are of the order of 1 GeV/c2, which makes the GeV (gigaelectronvolt) a convenient unit of mass for particle physics:

The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1 e, a spin of 1/2, and has the same mass as an electron. When a positron collides with an electron, annihilation occurs. If this collision occurs at low energies, it results in the production of two or more gamma ray photons.

In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons. The total energy and momentum of the initial pair are conserved in the process and distributed among a set of other particles in the final state. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of such an original pair are zero. Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy and conservation of momentum are obeyed.

A proton is a subatomic particle, symbol
p
or
p+
, with a positive electric charge of +1e elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collectively referred to as "nucleons".

1 GeV/c2 = 1.783×10−27 kg.

The unified atomic mass unit (u), 1 gram divided by Avogadro's number, is almost the mass of a hydrogen atom, which is mostly the mass of the proton. To convert to megaelectronvolts, use the formula:

1 u = 931.4941 MeV/c2 = 0.9314941 GeV/c2.

Momentum

In high-energy physics, the electronvolt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy (i.e., 1 eV). This gives rise to usage of eV (and keV, MeV, GeV or TeV) as units of momentum, for the energy supplied results in acceleration of the particle.

The dimensions of momentum units are LMT−1. The dimensions of energy units are L2MT−2. Then, dividing the units of energy (such as eV) by a fundamental constant that has units of velocity (LT−1), facilitates the required conversion of using energy units to describe momentum. In the field of high-energy particle physics, the fundamental velocity unit is the speed of light in vacuum c.

By dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/c. [7] [8]

The fundamental velocity constant c is often dropped from the units of momentum by way of defining units of length such that the value of c is unity. For example, if the momentum p of an electron is said to be 1 GeV, then the conversion to MKS can be achieved by:

${\displaystyle p=1\;{\text{GeV}}/c={\frac {(1\times 10^{9})\cdot (1.60217646\times 10^{-19}\;{\text{C}})\cdot (1\;{\text{V}})}{(2.99792458\times 10^{8}\;{\text{m}}/{\text{s}})}}=5.344286\times 10^{-19}\;{\text{kg}}\cdot {\text{m}}/{\text{s}}.}$

Distance

In particle physics, a system of "natural units" in which the speed of light in vacuum c and the reduced Planck constant ħ are dimensionless and equal to unity is widely used: c = ħ = 1. In these units, both distances and times are expressed in inverse energy units (while energy and mass are expressed in the same units, see mass–energy equivalence). In particular, particle scattering lengths are often presented in units of inverse particle masses.

Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:

${\displaystyle \hbar ={{h} \over {2\pi }}=1.054\ 571\ 726(47)\times 10^{-34}\ {\mbox{J s}}=6.582\ 119\ 28(15)\times 10^{-16}\ {\mbox{eV s}}.}$

The above relations also allow expressing the mean lifetime τ of an unstable particle (in seconds) in terms of its decay width Γ (in eV) via Γ = ħ/τ. For example, the B0 meson has a lifetime of 1.530(9)  picoseconds, mean decay length is = 459.7 μm, or a decay width of (4.302±25)×10−4 eV.

Conversely, the tiny meson mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.

Energy in electronvolts is sometimes expressed through the wavelength of light with photons of the same energy: 1 eV = 8065.544005(49) cm−1.

Temperature

In certain fields, such as plasma physics, it is convenient to use the electronvolt as a unit of temperature. The conversion to the Kelvin scale is defined by using kB, the Boltzmann constant:

${\displaystyle {1 \over k_{\text{B}}}={1.602\,176\,53(14)\times 10^{-19}{\text{ J/eV}} \over 1.380\,6505(24)\times 10^{-23}{\text{ J/K}}}=11\,604.505(20){\text{ K/eV}}.}$

For example, a typical magnetic confinement fusion plasma is 15 keV, or 170 MK.

As an approximation: kBT is about 0.025 eV (≈ 290 K/11604 K/eV) at a temperature of 20 °C.

Properties

The energy E, frequency v, and wavelength λ of a photon are related by

${\displaystyle E=h\nu ={\frac {hc}{\lambda }}}$${\displaystyle ={\frac {(4.13566\,7516\times 10^{-15}\,{\mbox{eV}}\,{\mbox{s}})(299\,792\,458\,{\mbox{m/s}})}{\lambda }}}$

where h is the Planck constant, c is the speed of light. This reduces to

${\displaystyle E{\mbox{(eV)}}=4.13566\,7516\,{\mbox{feVs}}\cdot \nu \ {\mbox{(PHz)}}}$${\displaystyle ={\frac {1\,239.84193\,{\mbox{eV}}\,{\mbox{nm}}}{\lambda \ {\mbox{(nm)}}}}.}$ [9]

A photon with a wavelength of 532 nm (green light) would have an energy of approximately 2.33 eV. Similarly, 1 eV would correspond to an infrared photon of wavelength 1240 nm or frequency 241.8 THz.

Scattering experiments

In a low-energy nuclear scattering experiment, it is conventional to refer to the nuclear recoil energy in units of eVr, keVr, etc. This distinguishes the nuclear recoil energy from the "electron equivalent" recoil energy (eVee, keVee, etc.) measured by scintillation light. For example, the yield of a phototube is measured in phe/keVee (photoelectrons per keV electron-equivalent energy). The relationship between eV, eVr, and eVee depends on the medium the scattering takes place in, and must be established empirically for each material.

Energy comparisons

• 5.25×1032 eV: total energy released from a 20  kt nuclear fission device
• 1.22×1028 eV: the Planck energy
• 10 Y eV (1×1025 eV): the approximate grand unification energy
• ~624 E eV (6.24×1020 eV): energy consumed by a single 100-watt light bulb in one second (100 W = 100 J/s6.24×1020 eV/s)
• 300 E eV (3×1020 eV = ~50  J ): [13] the so-called Oh-My-God particle (the most energetic cosmic ray particle ever observed)
• 2 PeV: two petaelectronvolts, the most high-energetic neutrino detected by the IceCube neutrino telescope in Antarctica [14]
• 14 TeV: the designed proton collision energy at the Large Hadron Collider (operated at about half of this energy since 30 March 2010, reached 13 TeV in May 2015)
• 1 TeV: a trillion electronvolts, or 1.602×10−7 J, about the kinetic energy of a flying mosquito [15]
• 125.1±0.2 GeV: the energy corresponding to the mass of the Higgs boson, as measured by two separate detectors at the LHC to a certainty better than 5 sigma [16]
• 210 MeV: the average energy released in fission of one Pu-239 atom
• 200 MeV: the average energy released in nuclear fission of one U-235 atom
• 17.6 MeV: the average energy released in the fusion of deuterium and tritium to form He-4; this is 0.41 PJ per kilogram of product produced
• 1 MeV (1.602×10−13 J): about twice the rest energy of an electron
• 13.6 eV: the energy required to ionize atomic hydrogen; molecular bond energies are on the order of 1 eV to 10 eV per bond
• 1.6 eV to 3.4 eV: the photon energy of visible light
• 1.1 eV: the energy EG required to break a covalent bond in silicon
• 720 meV: the energy EG required to break a covalent bond in germanium
• 25 meV: the thermal energy kBT at room temperature; one air molecule has an average kinetic energy 38 meV
• 230 µeV: the thermal energy kBT of the cosmic microwave background

Per mole

One mole of particles given 1 eV of energy has approximately 96.5 kJ of energy – this corresponds to the Faraday constant (F96485 C mol−1) where the energy in joules of N moles of particles each with energy X eV is X·F·N.

Notes and references

1. IUPAC Gold Book Archived 2009-01-03 at the Wayback Machine , p. 75
2. SI brochure, Sec. 4.1 Table 7 Archived July 16, 2012, at the Wayback Machine
3. "CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-22. 2014 CODATA recommended values
4. "CODATA Value: electron volt". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-22. 2014 CODATA recommended values
5. "Definitions of the SI units: Non-SI units". The NIST Reference on Constants, Units, and Uncertainty. National Institute of Standards and Technology. Retrieved 2018-07-01.
6. Barrow, J. D. "Natural Units Before Planck." Quarterly Journal of the Royal Astronomical Society 24 (1983): 24.
7. "Units in particle physics". Associate Teacher Institute Toolkit. Fermilab. 22 March 2002. Archived from the original on 14 May 2011. Retrieved 13 February 2011.
8. "Special Relativity". Virtual Visitor Center. SLAC. 15 June 2009. Retrieved 13 February 2011.
9. "CODATA Value: Planck constant in eV s". Archived from the original on 22 January 2015. Retrieved 30 March 2015.
10. What is Light? Archived December 5, 2013, at the Wayback Machine UC Davis lecture slides
11. Elert, Glenn. "Electromagnetic Spectrum, The Physics Hypertextbook". hypertextbook.com. Archived from the original on 2016-07-29. Retrieved 2016-07-30.
12. "Definition of frequency bands on". Vlf.it. Archived from the original on 2010-04-30. Retrieved 2010-10-16.
13. Open Questions in Physics. Archived 2014-08-08 at the Wayback Machine German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.
14. "A growing astrophysical neutrino signal in IceCube now features a 2-PeV neutrino". Archived from the original on 2015-03-19.
15. Glossary Archived 2014-09-15 at the Wayback Machine - CMS Collaboration, CERN
16. ATLAS; CMS (26 March 2015). "Combined Measurement of the Higgs Boson Mass in pp Collisions at √s=7 and 8 TeV with the ATLAS and CMS Experiments". Physical Review Letters. 114 (19): 191803. arXiv:. Bibcode:2015PhRvL.114s1803A. doi:. PMID   26024162.